Problem 13 - Elementary Algebra

Question

Perform the subtractions. $$ 0-(8) $$

Step-by-Step Solution

Answer

Answer: -8

Step 1: Set up the subtraction equation

In this problem, we are given: $$ 0 - (8) $$ The equation is already set up for us, so we can proceed to subtracting 8 from 0.

Step 2: Perform the subtraction

Let's now perform the subtraction: $$ 0 - 8 = -8 $$ When subtracting a positive number from a smaller number (in this case, 0), the result is a negative number. The magnitude of the result is equal to the difference between the numbers (8 in this case).

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero and are usually found to the left of zero on the number line. They are written with a minus sign (-) before them. Understanding negative numbers is important in performing operations like subtraction, especially when dealing with integers below zero. For example, in the subtraction of 0 - 8, the result is -8, which is a negative number. Here:

• The zero represents a neutral point on the number line.
• The 8 is a positive integer we subtract from zero.
• The resulting -8 shows that we have moved 8 units to the left of zero on the number line.

In real-life, negative numbers often represent deficits, like money owed or temperatures below freezing.

Arithmetic Equations

Arithmetic equations involve basic operations such as addition, subtraction, multiplication, and division. They are fundamental in solving mathematical problems. In a subtraction operation, we subtract one number from another. Arithmetic equations help us find the difference between these two numbers.
When the operation involves subtracting a positive number from a smaller number (e.g., 0 - 8), it results in a negative number.

• Start with the initial number, here it's 0.
• Subtract the given number, 8, from it.
• Calculate the result, in this case, getting -8.

This example highlights how arithmetic equations enable us to understand and solve everyday numerical problems by using basic operations.

Integer Operations

Integer operations include addition, subtraction, multiplication, and division performed on whole numbers, including both positive and negative numbers. Understanding integer operations is essential for solving equations that involve these numbers.
For subtraction involving integers, especially when negative results occur, several rules apply:

• When subtracting a larger positive integer from a smaller one (e.g., 0 - 8), the result is negative.
• The sign of the result matches that of the larger number being subtracted if the initial number is smaller.
• The absolute value of the outcome is the difference between the numbers.

By mastering integer operations, students can handle complex calculations across various contexts in mathematics and everyday situations.